1a and 2:
The crux is to realize that two moving, interacting electrons cannot be a
closed system. The concomitant fields will carry momentum/energy to other
particles. Newton's third law envisions a closed system of only two
interacting particles. In such cases, Fa/b = -Fb/a would be a corollary
to the axiom of conservation of momentum. IOW the axiomatic conservation
of momentum is the proper generalization of N3. N3 is a special case of
this axiom. Pedagogically, I continue to discover cons of mom from
Newton's laws, but eventually add "the rest of the story", replacing N3
with the cons of mom.
PS. I introduce N3 as a "root model" to account for the observed
impossibility of a compound object to accelerate itself. I spend
considerable class time entertaining student conjectures of possible
"miracles" if we had objects which violated N3 (E.g. Fa/b>0 but Fb/a =
0).
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "Carl E. Mungan" <mungan@USNA.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, May 09, 2003 11:14 AM
Subject: conservation of momentum (was Re: Heat as an indestructible
substance)
| On Wednesday, May 7, 2000, Bob Sciamanda wrote:
|
| > I refer to our discovery and development of the conservation
| > of momentum. It was first derived (and still is in textbooks)
| > from Newton's laws of motion, a crucial premise being the
| > third law. With the discovery of the magnetic force between
| > moving charges, it was realized that there were forces that
| > did not obey Newton's third law. Surprisingly, this did not
| > invalidate our conservation of momentum conclusion - we
| > merely raised it to the level of an a-priori hypothesis, assigned
| > the missing momentum to the electromagnetic field, and
| > produced a consistent and testable model of particle interactions.
|
| This interesting paragraph prompts a variety of questions in my mind:
|
| 1a. Your example of magnetic force between moving charges is clear. I
| suppose "radiation pressure" would be another. Is it safe to say in
| general that "field forces" can violate Newton's third law (N3) but
| "contact forces" (speaking classically) cannot?
|
| 1b. Is it possible to patch up conservation of momentum so that it is
| *always* particle-like by quantizing the relevant fields, ie.
| introduce photons, gravitons, etc?
|
| 2. In parentheses you added "(and still is in textbooks)." Does this
| mean you think what textbooks are doing is a bit deceiving by virtue
| of pretending to rigorously derive conservation of momentum, when
| it's actually an inductive law?
|
| 3. I hope no one jumps on me for this, but I'll throw it out anyway.
| When it comes to energy, one has the pseudowork-energy (W-E) theorem
| which one can rigorously derive by spatially integrating N2. Then one
| has the broader conservation of energy law which includes W-E as a
| special case, but has been broadened beyond this by consideration of
| fields, internal energy, heat, etc. Could one choose to say the same
| about momentum: One can derive a "pseudoimpulse-momentum" theorem
| that applies to classical masses interacting by contact forces, but
| the broader conservation law also handles fields, waves, etc.
|
| Any additional thoughts anyone would like to add about conservation
| of momentum and how we discuss it in intro physics would be very
| welcome. I confess to never having thought about this clearly enough
| before. Carl
| --
| Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
| U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
| mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/